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Topology Discovery of Sparse Random Graphs With Few Participants ∗ (2011)
| Citations: | 3 - 0 self |
BibTeX
@MISC{An11topologydiscovery,
author = {Animashree An and Avinatan Hassidim and Jonathan Kelner},
title = {Topology Discovery of Sparse Random Graphs With Few Participants ∗},
year = {2011}
}
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Abstract
We considerthe taskoftopologydiscoveryofsparserandomgraphsusing end-to-endrandom measurements(e.g., delay)between a subset ofnodes, referredto as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants.
Keyphrases
sparse random graph topology discovery sub-linear number participant exchange message small number consistent reconstruction original random node participate consistent discovery accurate discovery second shortest path edit distance end-to-end information end-to-endrandom measurement sub-linear edit-distance guarantee subset ofnodes significant number algorithm result end-to-end measurement
